The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

The ``Outside-In'' Outburst of HT Cassiopeiae

We present results from photometric observations of the dwarf nova system HT Cas during the eruption of November 1995. The data include the first two--colour observations of an eclipse on the rise to outburst. They show that during the rise to outburst the disc deviates significantly from steady state models, but the inclusion of an inner-disc truncation radius of about 4 $R_{wd}$ and a ``flared'' disc of semi-opening angle of $10^{\circ}$ produces acceptable fits. The disc is found to have expanded at the start of the outburst to about $0.41R_{L1}$, as compared to quiescent measurements. The accretion disc then gradually decreases in radius reaching $<0.32R_{L1}$ during the last stages of the eruption. Quiescent eclipses were also observed prior to and after the eruption and a revised ephemeris is calculated.Comment: 9 pages, 11 figures, to appear in MNRA

Personal and social norms for food portion sizes in lean and obese adults.

BACKGROUND: Portion size is an important component of dietary advice for weight control, but little is known about what portion sizes people consider 'normal'. This study determined the effect of body mass index (BMI), gender, dietary restraint and liking of the food on personal and social portion size norms for a range of foods and the degree of certainty over the norms. METHODS: Thirty lean (BMI 20-25 kg m(-)(2)) and 30 obese (BMI 30-35 kg m(-)(2)) men and women (aged 18-60 years) viewed 17 different portion sizes of 12 foods on a computer screen on two occasions a week apart. Participants responded 'more' or 'less' to each photograph reflecting personal portion size preference or perceived portion sizes of others. Personal and social norms for portion sizes of each food were determined using the method of constant stimuli giving a sigmoidal curve of the probability of answering 'less' over a range of portion sizes. The slope of the sigmoid at the norm gave a measure of certainty about the norm. Regression models were used to examine the effect of BMI, gender, dietary restraint and liking of the food on personal norms, social norms, the relationship between norms, and the slopes. RESULTS: Personal norms were significantly larger in the obese (P=0.026), men (P<0.001), those with lower dietary restraint (P<0.001), and those with higher liking for the food (P<0.001). Social norms were larger for women (P=0.012). The slopes at the norms were 30% shallower in the obese and in men (P<0.001). CONCLUSION: Larger personal norms for portion size among the obese, men, those with lower dietary restraint and those with higher liking for a food imply greater consumption, which may undermine weight control. Shallower slopes for norms in the obese and in men may imply less clearly defined habitual portion sizes.This study was supported by a program grant from the UK Medical Research Council (U105960389).This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/ijo.2015.4

Walking For Health: A Community Education and Physical Activity Initiative

Background/Introduction: Vermont was ranked the nation’s healthiest state, according to 2007 America’s Health Rankings. However obesity, currently the second most common cause of death among VT adults, is becoming so common it may replace cigarette smoking as the number one risk factor for death. In fact obesity affects 21% of adults in VT, most commonly low income adults. Obesity is a risk factor for high cholesterol, high blood pressure, heart diseases, and diabetes. Diet quality and physical activity are important factors in preventing obesity. 42% of Vermont adults are below the recommended level of physical activity. Greater knowledge about nutrition correlates with improved diet quality and greater physical activity. A successful educational strategy on physical activity and nutrition promotes group activities and adapts for cultural relevance.https://scholarworks.uvm.edu/comphp_gallery/1013/thumbnail.jp

Examining the moderating effect of individual-level cultural values on users’ acceptance of E-learning in developing countries: a structural equation modeling of an extended technology acceptance model

In this study, we examine the effects of individual-level culture on the adoption and acceptance of e-learning tools by students in Lebanon using a theoretical framework based on the Technology Acceptance Model (TAM). To overcome possible limitations of using TAM in developing countries, we extend TAM to include subjective norms (SN) and quality of work life constructs as additional constructs and a number of cultural variables as moderators. The four cultural dimensions of masculinity/femininity (MF), individualism/collectivism, power distance and uncertainty avoidance were measured at the individual level to enable them to be integrated into the extended TAM as moderators and a research model was developed based on previous literature. To test the hypothesised model, data were collected from 569 undergraduate and postgraduate students using e-learning tools in Lebanon via questionnaire. The collected data were analysed using the structural equation modelling technique in conjunction with multi-group analysis. As hypothesised, the results of the study revealed perceived usefulness (PU), perceived ease of use (PEOU), SN and quality of work life to be significant determinants of students’ behavioural intention (BI) towards e-learning. The empirical results also demonstrated that the relationship between SN and BI was particularly sensitive to differences in individual-cultural values, with significant moderating effects observed for all four of the cultural dimensions studied. Some moderating effects of culture were also found for both PU and PEOU, however, contrary to expectations the effect of quality of work life was not found to be moderated by MF as some previous authors have predicted. The implications of these results to both theory and practice are explored in the paper

Organic aerosol formation downwind from the Deepwater Horizon oil spill.

A large fraction of atmospheric aerosols are derived from organic compounds with various volatilities. A National Oceanic and Atmospheric Administration (NOAA) WP-3D research aircraft made airborne measurements of the gaseous and aerosol composition of air over the Deepwater Horizon (DWH) oil spill in the Gulf of Mexico that occurred from April to August 2010. A narrow plume of hydrocarbons was observed downwind of DWH that is attributed to the evaporation of fresh oil on the sea surface. A much wider plume with high concentrations of organic aerosol (&gt;25 micrograms per cubic meter) was attributed to the formation of secondary organic aerosol (SOA) from unmeasured, less volatile hydrocarbons that were emitted from a wider area around DWH. These observations provide direct and compelling evidence for the importance of formation of SOA from less volatile hydrocarbons